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## #1 2012-10-15 15:58:02

Agnishom
Real Member

Online

### Integer Factorisation

Prove the following:
If:

where p are prime numbers
Then:

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda

## #2 2012-10-15 20:54:41

scientia
Full Member

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### Re: Integer Factorisation

#### Agnishom wrote:

Prove the following:
If:

where p are distinct prime numbers
Then:

Let
denote the number of positive factors of
.

It's obvious that if
and
have no factor in common other than ±1, then
.

Also the factors of
are
and so
.

Combining the two observations above gives the required solution.

## #3 2012-10-15 21:29:19

bob bundy
Moderator

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### Re: Integer Factorisation

hi scientia

Nice proof!

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #4 2012-10-15 22:05:15

Agnishom
Real Member

Online

### Re: Integer Factorisation

Thanks @scientia

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda